cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A184593 5n - A101306: sum_{i=1..n} the last digit of prime(i).

Original entry on oeis.org

3, 5, 5, 3, 7, 9, 7, 3, 5, 1, 5, 3, 7, 9, 7, 9, 5, 9, 7, 11, 13, 9, 11, 7, 5, 9, 11, 9, 5, 7, 5, 9, 7, 3, -1, 3, 1, 3, 1, 3, -1, 3, 7, 9, 7, 3, 7, 9, 7, 3, 5, 1, 5, 9, 7, 9, 5, 9, 7, 11, 13, 15, 13, 17, 19, 17, 21, 19, 17, 13, 15, 11, 9, 11, 7, 9, 5, 3, 7, 3
Offset: 1

Views

Author

Robert G. Wilson v, Jan 17 2011

Keywords

Comments

The differences are always odd since the parity of A101306 and n are always opposite.
Positions where a(n)=2k-1 for k>0; 10, 1, 2, 5, 6, 20, 21, 62, 64, 65, 67, 198, 761, 765, 764, 800, ... - Robert G. Wilson v, Jun 06 2012

Crossrefs

Cf. A101306, A122754, A184594.

Programs

  • Mathematica
    f[n_] := 5n - Sum[ Mod[ Prime@ k, 10], {k, n}]; Array[f, 80]
Rest@ FoldList[# + 5 - Mod[Prime@ #2, 10] &, 0, Range@ 80]

Formula

a(n) = 5*n - Sum_{i=1..n} Prime(i) (mod 10).

A122754 a(n) = 10*n - A101306(n).

Original entry on oeis.org

8, 15, 20, 23, 32, 39, 42, 43, 50, 51, 60, 63, 72, 79, 82, 89, 90, 99, 102, 111, 118, 119, 126, 127, 130, 139, 146, 149, 150, 157, 160, 169, 172, 173, 174, 183, 186, 193, 196, 203, 204, 213, 222, 229, 232, 233, 242, 249, 252, 253
Offset: 1

Views

Author

Roger L. Bagula, Sep 21 2006

Keywords

Crossrefs

Cf. A101306.
Partial sums of A072003.

Programs

  • Mathematica
    Table[Sum[10 - Mod[Prime[n], 10], {n, 1, m}], {m, 1, 50}]

Formula

a(n) = Sum_{i=1..n} (10 - A007652(n)).

Extensions

Definition simplified by the Assoc. Eds. of the OEIS, Mar 27 2010

A184594 Where A184593, the difference between 5n and A101306(n), becomes a new record in either direction.

Original entry on oeis.org

1, 2, 5, 6, 20, 21, 35, 62, 64, 65, 67, 97, 159, 198, 267, 444, 449, 499, 761, 764, 800, 801, 802, 803, 804, 810, 886, 1413, 1435, 1613, 1614, 1615, 1634, 2566, 2568, 4162, 4653, 6115, 6118, 6120, 6121, 6124, 6136, 7063, 7070, 7071, 7075, 7076, 7118, 7119, 7424
Offset: 1

Views

Author

Robert G. Wilson v, Jan 17 2011

Keywords

Comments

Use the first Mathematica program in A184593 to produce the difference.

Crossrefs

Cf. A184593.

Programs

  • Mathematica
    k = 1; p = 2; lst = {}; mn = mx = s = 0; While[p < 10^5, s = s + Mod[p, 10]; d = s - 5 k; If[ Positive@ d, If[d > mx, AppendTo[lst, k]; mx = d], If[d < mn, AppendTo[lst, k]; mn = d]]; k++; p = NextPrime@ p]; lst

A122755 Let f(m) = 10 - last digit of prime(m). Sequence gives numbers n such that (1/n)*Sum_{ m <= n } f(m) is <= 5.

Original entry on oeis.org

35, 41, 81, 93, 95, 97, 109, 114, 149, 151, 158, 159, 160, 161, 162, 163, 165, 169, 171, 176
Offset: 1

Views

Author

Roger L. Bagula, Sep 21 2006

Keywords

Comments

For some reason taking f(m) = last digit of prime(m) doesn't work.

Crossrefs

Cf. A101306.

Programs

  • Mathematica
    a = Flatten[Table[If[Sum[10 - Mod[Prime[n], 10], {n, 1, m}]/m <= 5, m, {}], {m, 1, 200}]]

Extensions

Edited by N. J. A. Sloane, Mar 30 2007
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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